An alternative approach that is very used in recent mathematical programming based problems is to construct objective functions to guide the optimization approach to obtain fair solutions. This is the case of the so-called \(\alpha \) -fairness [1]}, [2]}, [3]}, [4]}, [5]}. The \(\alpha \) -fairness functions were introduced by [6]} and was defined as the one maximizing the constant elasticity social welfare. This family of functions generalizes well-known criteria in the the allocation of resources, as the utilitarian principle (\(\alpha =0\) ), which is neutral toward inequalities; proportional fairness (\(\alpha =1\) ), that was introduced by [7]}; and for \(\alpha \rightarrow \infty \)  the measure converges to the max-min criterion. As we will observe, other possibilities of \(\alpha \)  allow to find a trade-off between efficiency and fairness, opening room for different and suitable allocation patterns.
